In[26]:= Eigensystem[\!\(\*
TagBox[
RowBox[{"(", GridBox[{
{"6", "2", "1"},
{"0", "4", "2"},
{"0", "0", "3"}
}], ")"}],
"Grid"]\)]
Out[26]= {{6, 4, 3}, {{1, 0, 0}, {-1, 1, 0}, {1, -2, 1}}}
In[27]:= Inverse[\!\(\*
TagBox[
RowBox[{"(", GridBox[{
{"1",
RowBox[{"-", "1"}], "1"},
{"0", "1",
RowBox[{"-", "2"}]},
{"0", "0", "1"}
}], ")"}],
"Grid"]\)] // MatrixForm
Out[27]//MatrixForm= \!\(
TagBox[
RowBox[{"(", "", GridBox[{
{"1", "1", "1"},
{"0", "1", "2"},
{"0", "0", "1"}
},
GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}}], "", ")"}],
Function[BoxForm`e$,
MatrixForm[BoxForm`e$]]]\)
In[2]:= \!\(\*
TagBox[
RowBox[{"(", "", GridBox[{
{"1", "1", "1"},
{"0", "1", "2"},
{"0", "0", "1"}
},
GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}}], "", ")"}],
Function[BoxForm`e$,
MatrixForm[BoxForm`e$]]]\) . ( \!\(\*
TagBox[GridBox[{
{
RowBox[{"e", "^",
RowBox[{"{",
RowBox[{"6", "t"}], "}"}]}], "0", "0"},
{"0",
RowBox[{"e", "^",
RowBox[{"{",
RowBox[{"4", "t"}], "}"}]}], "0"},
{"0", "0",
RowBox[{"e", "^",
RowBox[{"{",
RowBox[{"3", "t"}], "}"}]}]}
}],
"Grid"]\) ) . ( {
{1, -1, 1},
{0, 1, -2},
{0, 0, 1}
} ) . ( \!\(\*
TagBox[GridBox[{
{"x"},
{"y"},
{"z"}
}],
"Grid"]\) )
Out[2]= {{1, 1, 1}, {0, 1, 2}, {0, 0, 1}} . \!\(\*
TagBox[GridBox[{
{
RowBox[{"{",
SuperscriptBox["e",
RowBox[{"6", " ", "t"}]], "}"}], "0", "0"},
{"0",
RowBox[{"{",
SuperscriptBox["e",
RowBox[{"4", " ", "t"}]], "}"}], "0"},
{"0", "0",
RowBox[{"{",
SuperscriptBox["e",
RowBox[{"3", " ", "t"}]], "}"}]}
},
AutoDelete->False,
GridBoxItemSize->{}],
"Grid"]\) . {{1, -1, 1}, {0, 1, -2}, {0, 0, 1}} . \!\(\*
TagBox[GridBox[{
{"x"},
{"y"},
{"z"}
},
AutoDelete->False,
GridBoxItemSize->{}],
"Grid"]\)&[Wolfram Notebook][1]
